Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY ˇ DAVIS ˇ IRVINE ˇ LOS ANGELES ˇ MERCED ˇ RIVERSIDE ˇ SAN DIEGO ˇ SAN FRANCISCO
CSANTA BARBARA ˇ SANTA CRUZ
Geometry, Topology, and Physics Seminar
Organizational Meeting
Friday, September 26, 2008, 4:00 p.m.
Room 6635 South Hall
Abstract: This quarter, we will devote a large portion of the Geometry, Topology,
and Physics seminar to the study of so-called "wall-crossing formulas." Such formulas
first arose in the celebrated work of Seiberg and Witten, where they related the count
of "BPS quantum states" in one part of the moduli space (of certain quantum field
theories) to the count in another part of the moduli space: this led directly to a new
method for computing Donaldson invariants of 4-manifolds, and the rest is history.
There has been some dramatic recent progress in understanding this kind of formula
in other contexts, including cases where the curves on a Calabi­Yau manifold are
being counted. The ingredients for this progress include considerations of symplectic
geometry and a study of "Stokes factors" in differential equations. There is also a
beautiful physics argument for the wall-crossing formulas (in some cases), involving
a study of the 4-dimensional physical theory on R3
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